A Level Maths Surds help pls help

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#1
Can someone help me out and explain the rest of the solution to simplify
√12/√156

first off i rationalised the denominator since it is a fraction
√12×√156÷√156×√156
√12 = 2²×3 so √12= √4×√3 using the rule √a ×√b =√a×b √12= 2√3
√156=2²x39 so √156 =√4×√39 so for the numerator i get 2√3×2√39 for the denominator using the rule √a ×√a =a therefore √156×√156=156
so i have 2√3×2√39 ÷ 156 = collecting the 2×2=4 and then √3√39 i have
4√3√39/156 then cancelling the 4 as a common factor of top and bottom i get
√3√39/39 it is at this point i am stuck could someone explain the rest of the solution and explain the other steps pointing me in the right direction for future questions
0
6 days ago
#2
Before rationalising, I always look to see if I could simplify it further, as there may be some terms in the numerator and denominator that cancel each other out and make my job much easier.

You've already identified that √12= 2√3. Since 156 is divisible by 12 to get 13, you can simplify √156= √12√13= 2√3√13.
This gives you (√12 / √156) = ( 2√3 / 2√3√13) which, after cancelling like terms, = 1/√13

That's a nicer expression to rationalise, so you can take it from there. Hope that helps
0
#3
(Original post by 2014FHD)
Before rationalising, I always look to see if I could simplify it further, as there may be some terms in the numerator and denominator that cancel each other out and make my job much easier.

You've already identified that √12= 2√3. Since 156 is divisible by 12 to get 13, you can simplify √156= √12√13= 2√3√13.
This gives you (√12 / √156) = ( 2√3 / 2√3√13) which, after cancelling like terms, = 1/√13

That's a nicer expression to rationalise, so you can take it from there. Hope that helps
thank you very much
0
6 days ago
#4
(Original post by liamlarner)
Can someone help me out and explain the rest of the solution to simplify
√12/√156

first off i rationalised the denominator since it is a fraction
√12×√156÷√156×√156
√12 = 2²×3 so √12= √4×√3 using the rule √a ×√b =√a×b √12= 2√3
√156=2²x39 so √156 =√4×√39 so for the numerator i get 2√3×2√39 for the denominator using the rule √a ×√a =a therefore √156×√156=156
so i have 2√3×2√39 ÷ 156 = collecting the 2×2=4 and then √3√39 i have
4√3√39/156 then cancelling the 4 as a common factor of top and bottom i get
√3√39/39 it is at this point i am stuck could someone explain the rest of the solution and explain the other steps pointing me in the right direction for future questions
Yes, surely, by breaking down into factors, it's just
√12
----
√12 √13

so 1 / √13 and I would probably then multiply top and bottom by √13 to get the surd off the bottom.
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